ffsshhttiikk What I do
- Solve Schrödinger equation for various potentials
- Analyze quantum mechanical operators and observables
- Model quantum tunneling and barrier penetration
- Calculate expectation values and probability distributions
- Study angular momentum and spin systems
- Apply perturbation theory for approximate solutions
When to use me
When analyzing atomic, molecular, or subatomic systems, or designing quantum devices.
Key Concepts
- Schrödinger Equation: iℏ∂ψ/∂t = Ĥψ, time-independent: Ĥψ = Eψ
- Wave Function: |ψ|² gives probability density, normalized ∫|ψ|²dτ = 1
- Uncertainty Principle: ΔxΔp ≥ ℏ/2, ΔEΔt ≥ ℏ/2
- Quantum Harmonic Oscillator: E_n = (n + ½)ℏω, quantized energy levels
- Tunneling: Probability T ≈ e^{-2γd} through potential barriers
- Spin: s = ½ for electrons, Pauli exclusion principle for fermions